Quasi-multipliers on group algebras related to a locally compact group

Abstract

In this paper, we first characterize quasi-multipliers of $(M({\cal G})_0^*)^*$ and show that the Banach algebra of all quasi-multipliers of $(M({\cal G})_0^*)^*$ is isometrically isomorphic to $(M({\cal G})_0^*)^*$. We also establish that quasi-multipliers of $(M({\cal G})_0^*)^*$ are separately continuous. Then, we investigate the existence of weakly compact quasi-multipliers of $(M({\cal G})_0^*)^*$. Finally, we prove that the Banach algebra of quasi-multipliers of $(M({\cal G})_0^*)^*$  is commutative if and only if ${\cal G}$ is abelian and discrete.